The two most senior members of the health regulator at the centre of cover-up allegations involving baby deaths in Cumbria have been finally named.

In a letter to the health secretary, Jeremy Hunt, the current chair and chief executive of the Care Quality Commission, David Prior, singled out former chief executive Cynthia Bower, her deputy, Jill Finney, as well as a press officer, Anna Jefferson, who were in apparent agreement over the need to "delete" a report critical of the regulator's investigation into University Hospitals of Morecambe Bay foundation trust.

The CQC said it was seeking advice on whether "there is an appropriate action that might be taken in relation to named individuals".

Up to 16 babies and two mothers are feared to have died between 2001 and 2012 because of poor care at the maternity unit at the Barrow-in-Furness hospital, part of the trust. Controversially, when the report was published the names were redacted.

It emerged that Bower, who left the regulator last year with a £1.4m pension pot, resigned on Thursday as a non-executive director of Skills for Health, an organisation which acts as the voice of healthcare employers in the skills system. Finney, now chief operating officer of internet company Nominet, was "not in the office today". Both Bower and Finney deny the allegations.

Bower said that she "gave no instruction to delete" the internal review, but added that as the former boss of the healthcare watchdog: "The buck stops with me."

The political pressure had been mounting on the health regulator to reverse its decision to redact names from a damning report by the City consultants Grant Thornton after the information commissioner said the data protection act was no barrier to being transparent.

In the letter to Hunt, the CQC says it had reviewed the issues and that "in the light of this further consideration, we have come to the view that the overriding public interest in transparency and accountability gives us sufficient grounds to disclose the names of the individuals who were anonymised in the report".

It can now revealed that the head of regulatory risk and quality, Louise Dineley, raised the critical internal review at a meeting on 12 March last year at the regulator's London office.

She confronted Bower, Finney and Jefferson with evidence she had gathered of how the organisation had failed. However, Dineley says she was given an instruction by Finney "to delete [her] report and that Bower and Jefferson supported her in this".

The Grant Thornton report said the reason for Finney "giving this instruction was that the report was damaging for the CQC and posed an FoI [freedom of information] risk". Dineley claimed that Finney said to her "'Read my lips' when [she] gave [her] the instruction".

In the report Bower said she had no recollection of the meeting. Jefferson told Grant Thornton that "she could not say whether the instruction was given but if it had been [she] could not think why [she] had not acted upon it". In interviews Finney claimed she could not remember as far back as March 2012.

But Dineley produced a handwritten contemporaneous note of the meeting to support her allegations. Grant Thornton said that "of the four accounts we were given during the course of the of our enquiries, we find [Dineley's] version the most reliable".